We study in this paper the localization of the electric field and the dielectric properties of thin metal-dielectric composites at the percolation threshold. In particular, the effects of the loss in the metallic components are examined. To this end, such systems are modelled as random RL -C networks, and the local field distribution as well as the effective conductivity are determined by using an exact resolution of Kirchhoff equations in addition to a real-space renormalization group method for comparison. We find a delocalization of the eigenmodes which remain weakly localized for vanishing losses. This result seems to be in agreement with the anomalous absorption observed experimentally for such systems.

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In this paper we use a variant of the Watts-Strogatz small-world model to predict wildfire behavior near the critical propagation/nonpropagation threshold. We find that forest fire patterns are fractal and that critical exponents are universal, which suggests that the propagation/nonpropagation transition is a second-order transition. Universality tells us that the characteristic critical behaviour of propagation in real (amorphous) forest landscapes can be extracted from the simplest network model.

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